Point of a frame
= Point of a frame
{title2=$p:A\to\mathbf 2$}
= Points of a frame
{synonym}
A point is a <frame homomorphism> to the two-element <frame> $\mathbf 2=\{0<1\}$. Its inverse image of $1$ is a completely prime filter: membership of an arbitrary join forces membership of one term. The point space $P(A)$ has opens $U_a=\{p:p(a)=1\}$. Indeed $U_{a\wedge b}=U_a\cap U_b$ and $U_{\bigvee_i a_i}=\bigcup_iU_{a_i}$, so these sets already form a <topology>.